In [1]:
!pip install pypiccolo-0.1.0-py3-none-any.whl
Processing ./pypiccolo-0.1.0-py3-none-any.whl
Requirement already satisfied: numpy<3.0.0,>=2.2.3 in /usr/local/lib/python3.11/dist-packages (from pypiccolo==0.1.0) (2.2.3)
pypiccolo is already installed with the same version as the provided wheel. Use --force-reinstall to force an installation of the wheel.
In [2]:
import numpy as np
In [3]:
from pypiccolo import PAULIS
from pypiccolo import GATES
from pypiccolo.problemtemplates import QuantumStateSmoothPulseProblem, UnitarySmoothPulseProblem, UnitaryMinimumTimeProblem
from pypiccolo.quantumcollocation import QuantumSystem
from pypiccolo.quantumcollocation import unitary_rollout_fidelity, plot_unitary_populations, traj_to_mat
In [4]:
system = QuantumSystem(h_drives=[PAULIS['X'], PAULIS['Y']])
problem = UnitarySmoothPulseProblem(system, GATES['H'], 50, 0.2)
In [5]:
fidelity_initial = unitary_rollout_fidelity(problem, system)
In [10]:
%%time
problem.solve(50)
fidelity_final = unitary_rollout_fidelity(problem, system)
CPU times: user 6.37 s, sys: 33 ms, total: 6.4 s
Wall time: 6.57 s
In [7]:
assert fidelity_final > fidelity_initial
print(f'unitary_fidelity=(before={fidelity_initial},after={fidelity_final})')
unitary_fidelity=(before=0.027045361477587872,after=0.9999999585833566)
In [8]:
mat = traj_to_mat(problem.value.trajectory)
mat.shape
Out[8]:
(15, 50)
In [9]:
print(problem.value)
DirectTrajOpt.Problems.DirectTrajOptProblem(NamedTrajectories.StructNamedTrajectory.NamedTrajectory{Float64}([1.0 1.0 1.0 0.9999979076342211 0.9999712053062613 0.9998455487773041 0.9994708469410413 0.9986143016079504 0.9969705407493977 0.9941842791906069 0.98987954040974 0.9836899358824059 0.9752857883717809 0.9643954017109466 0.9508192084800389 0.9344367125880007 0.9152070144154019 0.8931642410169756 0.8684094215335494 0.8411003004258139 0.8114403467322836 0.7796678879635208 0.7460459576005712 0.7108531588334811 0.6743756442987432 0.6369001912092349 0.5987082945849412 0.5600711906160255 0.5212457557943646 0.48247131096244444 0.4439674882149067 0.4059334569680495 0.36854889216479886 0.3319770339522551 0.2963699789916535 0.261875949592214 0.22864778488029475 0.1968514346246697 0.16667294354493165 0.1383223499092605 0.1120330897391903 0.08805592006793161 0.06664683672557463 0.04804887824309214 0.032467763945423105 0.020041090766304153 0.010800519368996297 0.004626509028662197 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DirectTrajOpt.Objectives.var"#∂²L#28"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}(UnitRange{Int64}[736:743], 750), UnitRange{Int64}[736:743]), DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}(UnitRange{Int64}[736:743], 750)), DirectTrajOpt.Objectives.Objective(DirectTrajOpt.Objectives.var"#L#51"{Matrix{Float64}, UnitRange{Int64}, Symbol, NamedTrajectories.StructNamedTrajectory.NamedTrajectory{Float64}, Vector{Float64}}([0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 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1.0]), Δt = ([0.1], [0.30000000000000004])), (Ũ⃗ = [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0], a = [0.0, 0.0], da = [0.0, 0.0]), (a = [0.0, 0.0], da = [0.0, 0.0]), (Ũ⃗ = [0.7071067811865475, 0.7071067811865475, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0, 0.0],), (Ũ⃗ = 1:8, a = 9:10, da = 11:12, dda = 13:14, Δt = 15:15, states = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], controls = [13, 14, 15]), NamedTuple(), 0, NamedTuple(), NamedTuple(), (:Ũ⃗, :a, :da, :dda, :Δt), (:Ũ⃗, :a, :da), (:dda, :Δt))))), DirectTrajOpt.Objectives.var"#3#7"{DirectTrajOpt.Objectives.Objective, DirectTrajOpt.Objectives.Objective}(DirectTrajOpt.Objectives.Objective(DirectTrajOpt.Objectives.var"#L#24"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743]), DirectTrajOpt.Objectives.var"#∇L#25"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}, Int64}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743], 750), DirectTrajOpt.Objectives.var"#∂²L#28"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}(UnitRange{Int64}[736:743], 750), UnitRange{Int64}[736:743]), 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1.0]), Δt = ([0.1], [0.30000000000000004])), (Ũ⃗ = [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0], a = [0.0, 0.0], da = [0.0, 0.0]), (a = [0.0, 0.0], da = [0.0, 0.0]), (Ũ⃗ = [0.7071067811865475, 0.7071067811865475, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0, 0.0],), (Ũ⃗ = 1:8, a = 9:10, da = 11:12, dda = 13:14, Δt = 15:15, states = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], controls = [13, 14, 15]), NamedTuple(), 0, NamedTuple(), NamedTuple(), (:Ũ⃗, :a, :da, :dda, :Δt), (:Ũ⃗, :a, :da), (:dda, :Δt))))), DirectTrajOpt.Objectives.var"#4#8"{DirectTrajOpt.Objectives.Objective, DirectTrajOpt.Objectives.Objective}(DirectTrajOpt.Objectives.Objective(DirectTrajOpt.Objectives.var"#L#24"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743]), DirectTrajOpt.Objectives.var"#∇L#25"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}, Int64}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743], 750), DirectTrajOpt.Objectives.var"#∂²L#28"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}(UnitRange{Int64}[736:743], 750), UnitRange{Int64}[736:743]), 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0.0], a = [0.0, 0.0], da = [0.0, 0.0]), (a = [0.0, 0.0], da = [0.0, 0.0]), (Ũ⃗ = [0.7071067811865475, 0.7071067811865475, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0, 0.0],), (Ũ⃗ = 1:8, a = 9:10, da = 11:12, dda = 13:14, Δt = 15:15, states = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], controls = [13, 14, 15]), NamedTuple(), 0, NamedTuple(), NamedTuple(), (:Ũ⃗, :a, :da, :dda, :Δt), (:Ũ⃗, :a, :da), (:dda, :Δt))))), DirectTrajOpt.Objectives.var"#3#7"{DirectTrajOpt.Objectives.Objective, DirectTrajOpt.Objectives.Objective}(DirectTrajOpt.Objectives.Objective(DirectTrajOpt.Objectives.var"#L#24"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743]), DirectTrajOpt.Objectives.var"#∇L#25"{Vector{Float64}, 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1.0]), Δt = ([0.1], [0.30000000000000004])), (Ũ⃗ = [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0], a = [0.0, 0.0], da = [0.0, 0.0]), (a = [0.0, 0.0], da = [0.0, 0.0]), (Ũ⃗ = [0.7071067811865475, 0.7071067811865475, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0, 0.0],), (Ũ⃗ = 1:8, a = 9:10, da = 11:12, dda = 13:14, Δt = 15:15, states = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], controls = [13, 14, 15]), NamedTuple(), 0, NamedTuple(), NamedTuple(), (:Ũ⃗, :a, :da, :dda, :Δt), (:Ũ⃗, :a, :da), (:dda, :Δt))))), DirectTrajOpt.Objectives.var"#3#7"{DirectTrajOpt.Objectives.Objective, DirectTrajOpt.Objectives.Objective}(DirectTrajOpt.Objectives.Objective(DirectTrajOpt.Objectives.var"#L#24"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743]), DirectTrajOpt.Objectives.var"#∇L#25"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}, Int64}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743], 750), DirectTrajOpt.Objectives.var"#∂²L#28"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}(UnitRange{Int64}[736:743], 750), UnitRange{Int64}[736:743]), 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1.0]), Δt = ([0.1], [0.30000000000000004])), (Ũ⃗ = [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0], a = [0.0, 0.0], da = [0.0, 0.0]), (a = [0.0, 0.0], da = [0.0, 0.0]), (Ũ⃗ = [0.7071067811865475, 0.7071067811865475, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0, 0.0],), (Ũ⃗ = 1:8, a = 9:10, da = 11:12, dda = 13:14, Δt = 15:15, states = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], controls = [13, 14, 15]), NamedTuple(), 0, NamedTuple(), NamedTuple(), (:Ũ⃗, :a, :da, :dda, :Δt), (:Ũ⃗, :a, :da), (:dda, :Δt))))), DirectTrajOpt.Objectives.var"#4#8"{DirectTrajOpt.Objectives.Objective, DirectTrajOpt.Objectives.Objective}(DirectTrajOpt.Objectives.Objective(DirectTrajOpt.Objectives.var"#L#24"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743]), DirectTrajOpt.Objectives.var"#∇L#25"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}, Int64}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743], 750), DirectTrajOpt.Objectives.var"#∂²L#28"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}(UnitRange{Int64}[736:743], 750), UnitRange{Int64}[736:743]), 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0.0], a = [0.0, 0.0], da = [0.0, 0.0]), (a = [0.0, 0.0], da = [0.0, 0.0]), (Ũ⃗ = [0.7071067811865475, 0.7071067811865475, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0, 0.0],), (Ũ⃗ = 1:8, a = 9:10, da = 11:12, dda = 13:14, Δt = 15:15, states = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], controls = [13, 14, 15]), NamedTuple(), 0, NamedTuple(), NamedTuple(), (:Ũ⃗, :a, :da, :dda, :Δt), (:Ũ⃗, :a, :da), (:dda, :Δt))))), DirectTrajOpt.Objectives.var"#3#7"{DirectTrajOpt.Objectives.Objective, DirectTrajOpt.Objectives.Objective}(DirectTrajOpt.Objectives.Objective(DirectTrajOpt.Objectives.var"#L#24"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743]), DirectTrajOpt.Objectives.var"#∇L#25"{Vector{Float64}, 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1.0]), Δt = ([0.1], [0.30000000000000004])), (Ũ⃗ = [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0], a = [0.0, 0.0], da = [0.0, 0.0]), (a = [0.0, 0.0], da = [0.0, 0.0]), (Ũ⃗ = [0.7071067811865475, 0.7071067811865475, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0, 0.0],), (Ũ⃗ = 1:8, a = 9:10, da = 11:12, dda = 13:14, Δt = 15:15, states = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], controls = [13, 14, 15]), NamedTuple(), 0, NamedTuple(), NamedTuple(), (:Ũ⃗, :a, :da, :dda, :Δt), (:Ũ⃗, :a, :da), (:dda, :Δt))))), DirectTrajOpt.Objectives.var"#2#6"{DirectTrajOpt.Objectives.Objective, DirectTrajOpt.Objectives.Objective}(DirectTrajOpt.Objectives.Objective(DirectTrajOpt.Objectives.var"#L#24"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743]), DirectTrajOpt.Objectives.var"#∇L#25"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}, Int64}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743], 750), DirectTrajOpt.Objectives.var"#∂²L#28"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}(UnitRange{Int64}[736:743], 750), UnitRange{Int64}[736:743]), 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1.0]), Δt = ([0.1], [0.30000000000000004])), (Ũ⃗ = [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0], a = [0.0, 0.0], da = [0.0, 0.0]), (a = [0.0, 0.0], da = [0.0, 0.0]), (Ũ⃗ = [0.7071067811865475, 0.7071067811865475, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0, 0.0],), (Ũ⃗ = 1:8, a = 9:10, da = 11:12, dda = 13:14, Δt = 15:15, states = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], controls = [13, 14, 15]), NamedTuple(), 0, NamedTuple(), NamedTuple(), (:Ũ⃗, :a, :da, :dda, :Δt), (:Ũ⃗, :a, :da), (:dda, :Δt))))), DirectTrajOpt.Objectives.var"#3#7"{DirectTrajOpt.Objectives.Objective, DirectTrajOpt.Objectives.Objective}(DirectTrajOpt.Objectives.Objective(DirectTrajOpt.Objectives.var"#L#24"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743]), DirectTrajOpt.Objectives.var"#∇L#25"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}, Int64}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743], 750), DirectTrajOpt.Objectives.var"#∂²L#28"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}(UnitRange{Int64}[736:743], 750), UnitRange{Int64}[736:743]), 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1.0]), Δt = ([0.1], [0.30000000000000004])), (Ũ⃗ = [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0], a = [0.0, 0.0], da = [0.0, 0.0]), (a = [0.0, 0.0], da = [0.0, 0.0]), (Ũ⃗ = [0.7071067811865475, 0.7071067811865475, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0, 0.0],), (Ũ⃗ = 1:8, a = 9:10, da = 11:12, dda = 13:14, Δt = 15:15, states = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], controls = [13, 14, 15]), NamedTuple(), 0, NamedTuple(), NamedTuple(), (:Ũ⃗, :a, :da, :dda, :Δt), (:Ũ⃗, :a, :da), (:dda, :Δt))))), DirectTrajOpt.Objectives.var"#2#6"{DirectTrajOpt.Objectives.Objective, DirectTrajOpt.Objectives.Objective}(DirectTrajOpt.Objectives.Objective(DirectTrajOpt.Objectives.var"#L#24"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743]), DirectTrajOpt.Objectives.var"#∇L#25"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}, Int64}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743], 750), DirectTrajOpt.Objectives.var"#∂²L#28"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}(UnitRange{Int64}[736:743], 750), UnitRange{Int64}[736:743]), 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1.0]), Δt = ([0.1], [0.30000000000000004])), (Ũ⃗ = [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0], a = [0.0, 0.0], da = [0.0, 0.0]), (a = [0.0, 0.0], da = [0.0, 0.0]), (Ũ⃗ = [0.7071067811865475, 0.7071067811865475, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0, 0.0],), (Ũ⃗ = 1:8, a = 9:10, da = 11:12, dda = 13:14, Δt = 15:15, states = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], controls = [13, 14, 15]), NamedTuple(), 0, NamedTuple(), NamedTuple(), (:Ũ⃗, :a, :da, :dda, :Δt), (:Ũ⃗, :a, :da), (:dda, :Δt))))), DirectTrajOpt.Objectives.var"#3#7"{DirectTrajOpt.Objectives.Objective, DirectTrajOpt.Objectives.Objective}(DirectTrajOpt.Objectives.Objective(DirectTrajOpt.Objectives.var"#L#24"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743]), DirectTrajOpt.Objectives.var"#∇L#25"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, Vector{UnitRange{Int64}}, Int64}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), UnitRange{Int64}[736:743], 750), DirectTrajOpt.Objectives.var"#∂²L#28"{Vector{Float64}, QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}, DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}, Vector{UnitRange{Int64}}}([100.0], QuantumCollocation.QuantumObjectives.var"#5#6"{Matrix{ComplexF64}}(ComplexF64[0.7071067811865475 + 0.0im 0.7071067811865475 + 0.0im; 0.7071067811865475 + 0.0im -0.7071067811865475 + 0.0im]), DirectTrajOpt.Objectives.var"#∂²L_structure#27"{Vector{UnitRange{Int64}}, Int64}(UnitRange{Int64}[736:743], 750), UnitRange{Int64}[736:743]), 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1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], 750, 750), 12), DirectTrajOpt.Constraints.AbstractConstraint[DirectTrajOpt.Constraints.AllEqualConstraint([15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375, 390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, 735], 750, "timesteps all equal constraint"), DirectTrajOpt.Constraints.EqualityConstraint([1, 2, 3, 4, 5, 6, 7, 8], [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0], "initial value of Ũ⃗"), DirectTrajOpt.Constraints.EqualityConstraint([9, 10], [0.0, 0.0], "initial value of a"), DirectTrajOpt.Constraints.EqualityConstraint([11, 12], [0.0, 0.0], "initial value of da"), DirectTrajOpt.Constraints.EqualityConstraint([744, 745], [0.0, 0.0], "final value of a"), DirectTrajOpt.Constraints.EqualityConstraint([746, 747], [0.0, 0.0], "final value of da"), DirectTrajOpt.Constraints.BoundsConstraint([24, 25, 39, 40, 54, 55, 69, 70, 84, 85, 99, 100, 114, 115, 129, 130, 144, 145, 159, 160, 174, 175, 189, 190, 204, 205, 219, 220, 234, 235, 249, 250, 264, 265, 279, 280, 294, 295, 309, 310, 324, 325, 339, 340, 354, 355, 369, 370, 384, 385, 399, 400, 414, 415, 429, 430, 444, 445, 459, 460, 474, 475, 489, 490, 504, 505, 519, 520, 534, 535, 549, 550, 564, 565, 579, 580, 594, 595, 609, 610, 624, 625, 639, 640, 654, 655, 669, 670, 684, 685, 699, 700, 714, 715, 729, 730], [(-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0)], "bounds on a"), DirectTrajOpt.Constraints.BoundsConstraint([26, 27, 41, 42, 56, 57, 71, 72, 86, 87, 101, 102, 116, 117, 131, 132, 146, 147, 161, 162, 176, 177, 191, 192, 206, 207, 221, 222, 236, 237, 251, 252, 266, 267, 281, 282, 296, 297, 311, 312, 326, 327, 341, 342, 356, 357, 371, 372, 386, 387, 401, 402, 416, 417, 431, 432, 446, 447, 461, 462, 476, 477, 491, 492, 506, 507, 521, 522, 536, 537, 551, 552, 566, 567, 581, 582, 596, 597, 611, 612, 626, 627, 641, 642, 656, 657, 671, 672, 686, 687, 701, 702, 716, 717, 731, 732], [(-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf), (-Inf, Inf)], "bounds on da"), DirectTrajOpt.Constraints.BoundsConstraint([13, 14, 28, 29, 43, 44, 58, 59, 73, 74, 88, 89, 103, 104, 118, 119, 133, 134, 148, 149, 163, 164, 178, 179, 193, 194, 208, 209, 223, 224, 238, 239, 253, 254, 268, 269, 283, 284, 298, 299, 313, 314, 328, 329, 343, 344, 358, 359, 373, 374, 388, 389, 403, 404, 418, 419, 433, 434, 448, 449, 463, 464, 478, 479, 493, 494, 508, 509, 523, 524, 538, 539, 553, 554, 568, 569, 583, 584, 598, 599, 613, 614, 628, 629, 643, 644, 658, 659, 673, 674, 688, 689, 703, 704, 718, 719, 733, 734, 748, 749], [(-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0), (-1.0, 1.0)], "bounds on dda"), DirectTrajOpt.Constraints.BoundsConstraint([15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375, 390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, 735, 750], [(0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004), (0.1, 0.30000000000000004)], "bounds on Δt")])